Consider a cold standby system with two identical components. Initially, one component is working while the other is in standby. The failure rate of the standby component is zero. After a failure of the working component, the standby component will become operational and the repair of failure component will be started. In this state, if the working component fails before the repair of the failed component, then the system will reach a failed state. If repair of the failed component is done before the failure of the working component, then it will be kept in the standby mode. Hence, the system reaches state 1 again. Figure 8-14 shows the state transition diagram for this system.

The reliability expression of this system is similar to the reliability expression of the two-component parallel system. The only difference is that here, s1 and s2 are the roots of the equation s2+s(2λ+μ)+λ2=0:

As in the case of the parallel system, the approximation to system reliability is:

Therefore: